Precision Synchronization Using Amplitude Measurements in 5G and 6G

ABSTRACT

Prior art includes complex clock synchronization in 5G and 6G based on precision time measurements and multiple message exchanges. Disclosed is a simpler synchronization procedure suitable for reduced-capability receivers as well as high-performance users. The base station can transmit a brief signal on a specific subcarrier, surrounded fore and aft by silent periods, and the receiver can measure the signals in the silent periods to detect intrusion of the signal into one or the other silent periods, thereby indicating a timing offset. Alternatively, the base station can transmit a brief signal spanning an interface between subsequent symbol-times, and the receiver can measure the energy received in the two symbol-times, thereby detecting an offset. In either case, and other versions disclosed, the receiver can calculate the size and direction of the clock offset by amplitude measurements, and apply a correction without further communications between the user device and the base station.

PRIORITY CLAIMS AND RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.18/098,290, entitled “Compact Timing Signal for Low-Complexity 5G/6GSynchronization”, filed Jan. 18, 2023, which claims the benefit of U.S.Provisional Patent Application Ser. No. 63/431,810, entitled “Mid-SymbolTimestamp Point for Precision Synchronization in 5G and 6G”, filed Dec.12, 2022, and U.S. Provisional Patent Application Ser. No. 63/476,032,entitled “Guard-Space Timestamp Point for Precision Synchronization in5G and 6G”, filed Dec. 19, 2022, and U.S. Provisional Patent ApplicationSer. No. 63/435,061, entitled “Compact Timing Signal for Low-Complexity5G/6G Synchronization”, filed Dec. 23, 2022, and U.S. Provisional PatentApplication Ser. No. 63/437,839, entitled “Ultra-Lean SynchronizationProcedure for 5G and 6G Networking”, filed Jan. 9, 2023, all of whichare hereby incorporated by reference in their entireties.

FIELD OF THE INVENTION

The disclosure pertains to synchronization of clocks using a wirelesssignal that indicates timing information.

BACKGROUND OF THE INVENTION

Wireless messages depend on tightly controlled timing, so that modulatedsignals will be received at the expected time with the correctfrequency. Distributing the timing information by cable is no longerfeasible, as many users are mobile or at least portable; hence the timesynchronization and clock rate are generally distributed in wirelessmessages. Due to the very high frequencies planned for in 5G and 6G,improved means are needed to enable user devices to synchronize theirtiming and frequency precisely, without excessive messaging andoverhead.

This Background is provided to introduce a brief context for the Summaryand Detailed Description that follow. This Background is not intended tobe an aid in determining the scope of the claimed subject matter nor beviewed as limiting the claimed subject matter to implementations thatsolve any or all of the disadvantages or problems presented above.

SUMMARY OF THE INVENTION

In a first aspect, there is a method for a user device of a wirelessnetwork to synchronize a clock of the user device with a clock of a basestation of the wireless network, the method comprising: receiving, fromthe base station, three temporally successive resource elementscomprising a first resource element, a second resource element, and athird resource element, of a resource grid comprising subcarriers infrequency and symbol-times in time; wherein the first resource elementcomprises a first signal, the second resource element comprises a secondsignal, and the third resource element comprises a third signal;measuring a first energy of the first signal, a second energy of thesecond signal, and a third energy of the third signal; determining asignal difference comprising the first energy minus the third energy;determining a ratio comprising the signal difference divided by thesecond energy; determining, according to the ratio, a timing offset; andcausing the clock of the user device to be synchronized with the clockof the base station by subtracting the timing offset from the clock ofthe user device.

In another aspect, there is a method for a user device of a wirelessnetwork to synchronize a clock of the user device with a clock of a basestation of the wireless network, the method comprising: receiving, fromthe base station, two temporally successive resource elements comprisinga first resource element and a second resource element, of a resourcegrid comprising subcarriers in frequency and symbol-times in time;wherein the first resource element comprises a first signal and thesecond resource element comprises a second signal; measuring a firstsigned amplitude of the first signal and a second signed amplitude ofthe second signal; determining a signal difference comprising the firstsigned amplitude minus the second signed amplitude, and a signal sumcomprising the first signed amplitude plus the second signed amplitude,wherein a signed amplitude is an average amplitude at a particularphase, averaged across a symbol-time; determining a ratio according tothe signal difference and the signal sum; determining, according to theratio, a timing offset; and causing the clock of the user device to besynchronized with the clock of the base station by subtracting thetiming offset from the clock of the user device.

In another aspect, there is a method for a receiver of a wirelessnetwork to synchronize with a base station of the wireless network, themethod comprising: receiving, from the base station, four temporallysuccessive resource elements comprising a first resource element, asecond resource element, a third resource element, and a fourth resourceelement of a resource grid comprising subcarriers in frequency andsymbol-times in time; wherein the first resource element comprises afirst signal, the second resource element comprises a second signal, thethird resource element comprises a third signal, and the fourth resourceelement comprises a fourth signal; measuring a first signed amplitude ofthe first signal, a second signed amplitude of the second signal, athird signed amplitude of the third signal, and a fourth signedamplitude of the fourth signal; determining a signal differencecomprising the second signed amplitude minus the third signed amplitude,and a signal sum comprising the second signed amplitude plus the thirdsigned amplitude; determining a ratio according to the signal differenceand the signal sum; determining, according to the ratio, a timingoffset; and causing the clock of the user device to be synchronized withthe clock of the base station by subtracting the timing offset from theclock of the user device.

This Summary is provided to introduce a selection of concepts in asimplified form. The concepts are further described in the DetailedDescription section. Elements or steps other than those described inthis Summary are possible, and no element or step is necessarilyrequired. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended foruse as an aid in determining the scope of the claimed subject matter.The claimed subject matter is not limited to implementations that solveany or all disadvantages noted in any part of this disclosure.

These and other embodiments are described in further detail withreference to the figures and accompanying detailed description asprovided below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times, according to some embodiments.

FIG. 1B is a schematic showing an exemplary embodiment of another timingsignal including three symbol-times, according to some embodiments.

FIG. 1C is a schematic showing an exemplary embodiment of yet anothertiming signal including three symbol-times, according to someembodiments.

FIG. 1D is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio, according tosome embodiments.

FIG. 1E is a flowchart showing an exemplary embodiment of a procedurefor performing synchronization, according to some embodiments.

FIG. 2A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times with edge enhancements, according tosome embodiments.

FIG. 2B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with edgeenhancements, according to some embodiments.

FIG. 3A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times and edge-pulses, according to someembodiments.

FIG. 3B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with edgepulses, according to some embodiments.

FIG. 4A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times and a ramped amplitude, according tosome embodiments.

FIG. 4B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with a rampedamplitude, according to some embodiments.

FIG. 5A is a schematic showing an exemplary embodiment of a timingsignal including two symbol-times and a uniform amplitude, according tosome embodiments.

FIG. 5B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with a uniformamplitude, according to some embodiments.

FIG. 6A is a schematic showing an exemplary embodiment of a timingsignal including two symbol-times and a phase-flip amplitude, accordingto some embodiments.

FIG. 6B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with aphase-flip amplitude, according to some embodiments.

FIG. 7A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times and a phase-flip amplitude,according to some embodiments.

FIG. 7B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with aphase-flip amplitude, according to some embodiments.

FIG. 8A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times, end-pulses, and a phase-flipamplitude, according to some embodiments.

FIG. 8B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio withend-pulses and a phase-flip amplitude, according to some embodiments.

Like reference numerals refer to like elements throughout.

DETAILED DESCRIPTION

Systems and methods disclosed herein (the “systems” and “methods”, alsooccasionally termed “embodiments” or “arrangements” or “versions” or“examples”, generally according to present principles) can provideurgently needed wireless communication protocols for preciselysynchronizing clocks using wireless signals configured to indicate aparticular time according to amplitude variations that a receiver canmeasure. Improved precision timing will be required for reliablecommunication at the high frequencies planned for 5G and 6G. Timingsignals disclosed herein may be configured to enable rapid precisiontime and frequency adjustment, according to some embodiments. Lean andefficient procedures are also disclosed for precise time adjustment,thereby avoiding unnecessary messaging and overhead, according to someembodiments.

Examples below include a brief timing signal spanning two or threesymbol-times. The timing signals include shaped amplitude regionsadjacent to regions of zero transmission. The timing signal is receivedby a receiver and analyzed according to the signals received in eachsymbol-time. The receiver's symbol boundaries are determined by thereceiver's system clock, but the timing signal itself is determined bythe transmitter's clock. Therefore, any disagreement between thetransmitter and receiver clocks causes the position of the timing signalto shift, relative to the receiver's symbol boundaries, which causes thesignal in one symbol-time to partially shift over into an adjacentsymbol-time. Hence the receiver can measure the clock disagreement bydetermining the amount of signal shifted over from a powered symbol-timeinto an adjacent unpowered symbol-time. Even a small amount of power maybe detected when it is shifted into the quiet symbol-time, therebyleading to high sensitivity, according to some embodiments.

Some wireless receivers have signal processing capabilities to detect abrief signal in an otherwise unpowered symbol-time. Other wirelessreceivers measure the average amplitude received at a particularsubcarrier during each symbol-time. The receiver may alternativelymeasure a power level or a received energy when a signal is present foronly a fraction of the symbol-time. To cover all of these modes ofreception, the amount of signal received in each symbol-time is referredto herein as the “measured amplitude” in each symbol-time, regardless ofhow the receiver measures the voltage or power or total energy or othertype of signal property. The important point is that the receiver candetermine the timing error by measuring amplitudes of signals insymbol-times, without the need to measure the times of timestampfeatures, and without exchanging legacy synchronization messages,thereby providing a substantial simplification at low/zero cost,according to some embodiments.

The receiver can quantify the timing disagreement by calculating a“signal ratio” R based on ratios of the measured amplitudes. In examplesbelow, the ratio equals zero when the receiver clock and the transmitterclock are synchronized, and R increases monotonically if they are notsynchronized. The signal ratio may thereby indicate whether the clocksare in disagreement, and by how much, and in which direction. In manycases, the receiver can determine timing disagreements more preciselyusing the signal ratio R, than with the legacy “first bit of firstoctet” procedures, according to some embodiments.

An advantage of the disclosed procedures may be that the base stationcan specify the synchronization schedule precisely in, for example, asystem information file such as an SSB or SIB1 message, thereby avoidingbulky synchronization messages of the prior art for each instance of thetiming signal. Another advantage may be that all of the user devices ina network can simultaneously synchronize their clock settings and clockfrequencies to the base station according to the schedule, whileavoiding unnecessary uplink transmissions. Another advantage may be thata receiver can determine a timing error based on amplitude measurementsalone, without requiring special signal processing to measure atimestamp point explicitly. Another advantage may be that the disclosedmethods employ the same amplitude-measuring capabilities that modernwireless receivers already have. Another advantage may be that thetiming information may be transferred in compact timing signals, eachspanning just two or three resource elements. Another advantage may bethat the disclosed timing signals may involve zero power transmissionduring a portion of the timing signals, thereby saving further power andavoiding contributing to backgrounds. Another advantage may be that thedisclosed timing signals, being compact and highly resource-efficient,may enable the base station to broadcast timing signals frequently (suchas once per frame or subframe) thereby enabling IOT user devices tomaintain sufficient synchronization even with low-cost oscillators fortiming, according to some embodiments.

Examples presented below are suitable for adoption by a wirelessstandards organization. Providing agreed-upon standards for the formatand interpretation of the a compact, precision timing signals disclosedherein may enable user devices to rapidly synchronize to the basestation, and may thereby optimize communication reliability at highfrequencies, without unnecessary messaging.

Terms herein generally follow 3GPP (third generation partnershipproject) standards, but with clarification where needed to resolveambiguities. As used herein, “5G” represents fifth-generation, and “6G”sixth-generation, wireless technology in which a network (or cell or LANLocal Area Network or RAN Radio Access Network or the like) may includea base station (or gNB or generation-node-B or eNB or evolution-node-Bor AP Access Point) in signal communication with a plurality of userdevices (or UE or User Equipment or user nodes or terminals or wirelesstransmit-receive units) and operationally connected to a core network(CN) which handles non-radio tasks, such as administration, and isusually connected to a larger network such as the Internet. Thetime-frequency space is generally configured as a “resource grid”including a number of “resource elements”, each resource element being aspecific unit of time termed a “symbol period” or “symbol-time”, and aspecific frequency and bandwidth termed a “subcarrier” (or “subchannel”in some references). Each symbol-time is bounded by symbol boundaries,according to a resource grid determined by a local clock. “OFDM symbols”(Orthogonal Frequency-Division Multiplexing) are symbol-times in whichthe individual signals of multiple subcarriers are added insuperposition. The time domain may be divided into ten-millisecondframes, one-millisecond subframes, and some number of slots, each slotincluding 14 symbol periods. The number of slots per subframe rangesfrom 1 to 8 depending on the “numerology” selected. The frequency axisis divided into “resource blocks” (also termed “resource element groups”or “REG” or “channels” in references) including 12 subcarriers, witheach subcarrier at a slightly different frequency. The “numerology” of aresource grid corresponds to the subcarrier spacing in the frequencydomain. Subcarrier spacings of 15, 30, 60, 120, and 240 kHz are definedin various numerologies. Each subcarrier can be independently modulatedto convey message information. Thus a resource element, spanning asingle symbol period in time and a single subcarrier in frequency, isthe smallest unit of a message. “SNR” (signal-to-noise ratio) and “SINR”(signal-to-interference-and-noise ratio) are used interchangeably unlessspecifically indicated. “RRC” (radio resource control) is a control-typemessage from a base station to a user device. “Digitization” refers torepeatedly measuring a waveform using, for example, a fast ADC(analog-to-digital converter) or the like. An “RF mixer” is a device formultiplying an incoming signal with a local oscillator signal, therebyselecting one component of the incoming signal. “IOT” orInternet-of-things refers to single-purpose wireless devices, usuallylow-performance. “SSB” (synchronization signal block) and SIB1 (systeminformation block 1) are system information messages.

In addition to the 3GPP terms, the following terms are defined. As usedherein, a “timing signal” is an RF (radio frequency) signal transmittedby a transmitter with a particular amplitude distribution configured toenable a receiver to detect timing disagreements between thetransmitter's clock and the receiver's clock. A receiver can detect thetiming signal, and determine the position (or time) of the amplitudevariations relative to the receiver's symbol boundaries according to thereceiver's clock. The receiver can then adjust its clock time accordingto the timing error thus measured, thereby synchronizing with the basestation. “Synchronization” means adjusting a clock setting to matchanother clock's time. Sequential symbol-times of a timing signal may betermed “S1”, “S2”. and “S3”, while the measured amplitudes in thosesymbol-times may be termed “A1”, “A2”, “A3” respectively.

Turning now to the figures, examples show how a reduced-capability userdevice can synchronize with a base station using amplitude measurementson a compact timing signal.

FIG. 1A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times, according to some embodiments. Asdepicted in this non-limiting example, a timing signal 101 is shownalong with part of a resource grid 102 which, in this case, spans threesuccessive symbol-times labeled S1, S2, and S3 at a particularsubcarrier (not labeled). The central symbol-time is indicated as 106.Each symbol-time is bounded by symbol boundaries 105. For regularmessaging, each symbol-time includes a guard-space 107 demarked by adashed line, and the remainder of the symbol-time is a message dataportion 108. However, the timing signals disclosed herein ignore thedistinction between guard-space 107 and message portion 108, insteadfilling each symbol-time 106 entirely with a particular amplitudesignal.

Also shown schematically is an amplitude envelope plot 103 indicatingthe timing signal 101 and the powered region 104, but with theoscillations suppressed. Thin lead lines are provided here andelsewhere, without label. The edges of the powered region 104 coincidewith the symbol-time boundaries 105 of the receiver's resource grid 102,thereby indicating that the receiver clock is synchronized with thetransmitter clock.

The timing signal 101 includes zero transmission in the firstsymbol-time S1, followed by a powered region 104 with non-zerotransmission in the second symbol-time S2, followed by a thirdsymbol-time S3 with zero transmission. The timing signal 101, includingthe times of the interfaces between the powered region 104 and thezero-amplitude regions, are determined by the transmitter clock. Thetimes of the symbol boundaries 105, however, are determined by thereceiver clock. If the receiver clock disagrees with the transmitterclock, the S2 symbol boundaries would be shifted relative to the timingsignal 101. Consequently, part of the non-zero transmission 104 would bereceived in one of the adjacent symbol-times S1 or S3, therebyindicating the timing error. The receiver can measure the amount ofsignal received, or the measured amplitude (A1, A2, A3) received, in thethree symbol-times. The receiver can then determine, according to aformula, a timing error relative to the transmitter clock. If thepowered region 104 is contained entirely within the S2 symbol boundaries105, then the timing error is zero and the two adjacent symbol-times S1S3 will have zero transmission. But if there is a disagreement betweenthe transmitter and receiver clocks, one of the adjacent symbol-times S1S3 will have a non-zero amplitude therein, which the receiver candetect.

To determine the timing error between the transmitter and receiverclocks, the receiver can subtract the signal values received in the twoouter symbol-times S1 and S3. If the receiver clock is in agreement withthe transmitter clock, the powered portion 104 will remain centered inthe central symbol-time S2, and hence A1 and A3 will remain at zeroamplitude, or at most a small and substantially equal energy content dueto backgrounds, so that the difference A3−A1 remains substantially zero.However, if the receiver clock is not in agreement with the transmitterclock, then the powered region 104 will be shifted relative to thereceiver's symbol boundaries 105, thus causing part of the poweredregion 104 to be shifted into either S1 or S3.

More generally, the receiver can determine the clock disagreement, or“timing error ΔT”, according to a formula based on the measuredamplitudes received A1, A2, and A3. The formula may be configured tocancel slowly-changing noise or interference. For example, the receivercan calculate a signal ratio R equal to a difference between themeasured amplitude in the two outer symbol-times divided by the measuredamplitude in the central symbol-time, or (A3−A1)/A2. This accentuatesany timing shift due to the receiver clock misalignment, while cancelingnoise that appears in the two outer symbol-times. Dividing by themeasured amplitude A2 in the central symbol-time is for normalization,since the absolute detection efficiency is generally unknown andirrelevant.

As an alternative, for improved linearity, the receiver can divide theA3−A1 difference by the sum of the magnitudes of the signals received inall three symbol-times, such as (A3−A1)/(|A1|−|A2|+|A3|). The verticalbars indicate the magnitude of the received signal. When so normalized,the signal ratio R is independent of the transmission level, gainsettings, efficiencies, etc. because those variables affect the all ofthe amplitudes A1, A2, and A3 values proportionally.

According to the ratio, the receiver can detect such a timing error, andcan determine whether the receiver's clock is fast or slow, and by howmuch. These determinations are based on amplitude measurements of thethree symbol-times, without the need for direct time measurements andwithout messaging, other than the compact timing signal itself.

The powered region 104 often includes a brief “ring-up” transition atthe start of the powered region 104, and a “ring-down” at the end, dueto finite bandwidth. This can introduce a small asymmetry in theresponses of S1 and S3. To minimize this asymmetry, the transmitter canapply extra power briefly at the start of the powered region 104, and areverse phase at the end of the powered region 104 to squelch theringdown. In addition, or alternatively, the receiver can calibrate theremaining asymmetry and subtract it from the amplitude measurements,before determining the timing error. Therefore the transition asymmetrywill be ignored hereinafter.

If the receiver clock disagrees with the transmitter clock, the timingshift may cause extraneous signals to encroach into S1 or S3 from theoutside, potentially obscuring the timing measurements. To avoid such aninterference, the receiver can ignore the first half of S1 and the lasthalf of S3, thereby discarding the encroaching signals. For example, thereceiver can integrate the measured amplitude in only the second half ofS1 and the first half of S3, thereby avoiding signal encroachment.Encroachment can still occur if the time disagreement is larger thanone-half the symbol period, but such large timing errors would berapidly detected by other effects such as message faults.

There is a possibility that a non-zero value of R may be due to a changein the propagation time of signals between the transmitter and receiver,due to motion or atmospheric effects, for example. When a recalibrationof the propagation time is needed, a round-trip travel-time test can beperformed, preferably using the timing signals disclosed herein forprecision and resource efficiency. In most applications, changes in thepropagation time occur on much longer time scales than clock drift, andtherefore the examples herein assume that any displacement of the timingsignal represents clock drift.

An advantage of the disclosed timing signal may be that all of the userdevices in a managed network can adjust their clock settings to the basestation, simultaneously, at no additional power expended or resourcesused. Each user device can determine its individual timing error and canadjust its local time-base as described. Hence the entire network ofuser devices can re-synchronize using a single compact timing signalthat consumes just three resource elements, with no further messaging oroverhead, according to some embodiments.

In addition to adjusting their clock times, the user devices cansimultaneously correct their clock rates (or frequency) by measuring adifference between two successive timing errors of two successive timingsignals. A change in the measured timing error is a sensitive measure ofa frequency or clock rate difference between the transmitter andreceiver clocks. The receiver frequency error is, to sufficientaccuracy, equal to the present frequency, times a difference in thetiming errors of two successive timing signals, divided by the intervalseparating them. Each user device can determine its frequency error andadjust its clock rate accordingly. Each user device can also correct itsclock time according to the first or second timing signal, as discussed.By this method, the user devices can adjust both their clock frequencyand their clock settings to synchronize with the base station.

The disclosed method can provide a rapid, lean, low-complexity, preciseclock synchronization, at a cost of just three resource elements (ofwhich only one is actually powered), according to some embodiments. Themethod involves only standard amplitude measurements, and hence avoidsspecial signal processing operations such as measuring a time of atimestamp point or other feature in the timing signal. Moreover, theprocedure avoids cumbersome prior-art messaging, as long as the receiverknows the periodicity or synchronization schedule of the timing signals.Embodiments of the disclosed method may therefore provide the enhancedsynchronization needed for fast-cadence 5G/6G communications.

FIG. 1B is a schematic showing an exemplary embodiment of another timingsignal including three symbol-times, according to some embodiments. Asdepicted in this non-limiting example, three symbol-times of a resourcegrid 112 include a timing signal 111 and an envelope plot 113. Theexample is similar to the previous case but now with a clockdisagreement. In this example, the powered portion 114 of the timingsignal 111 is now displaced by a displacement 117 relative to the symbolboundaries 115. A small portion of the powered region 114 therefore hasbeen shifted into the first symbol-time S1. The receiver can determinethe measured amplitude in S1, determine that it is greater than zero,and therefore determine that the receiver's clock disagrees with thetransmitter. Alternatively, the receiver can determine the displacementaccording to a function R of the signals received in S3 and S1, and cansynchronize its clock to the transmitter by subtracting the displacement117 from the receiver's clock setting. Subsequent downlink messagesshould then be aligned properly with the receiver's symbol boundaries115 without further timing corrections, according to some embodiments.

FIG. 1C is a schematic showing an exemplary embodiment of yet anothertiming signal including three symbol-times S1, S2, S3, according to someembodiments. As depicted in this non-limiting example, a timing signal121, with a powered region 124, is shifted relative to the symbolboundaries 125 in the receiver's resource grid 122, by a displacementamount 127. Also shown is the amplitude envelope 123. Unexpected signalpower or amplitude is therefore received in S3. The signal appearing inS3 indicates that the displacement 127 is opposite in sign from thedisplacement 117 of the previous example, and the size of the signalindicates that the displacement 127 is larger.

An extraneous message element 128, from an adjoining symbol-time, isencroaching into S1. To avoid interference from such encroachingsignals, the receiver is configured to discard any signal in the firsthalf of S1 and the last half of S3. Hence the receiver averages only thesignals within an analysis region 126, which includes the second half ofS1 and the first half of S3 (as well as the central symbol-time S2),while discarding the outer halves of S1 and S3. The ratio R is thereforeunaffected by the encroaching signal 128 because it is outside theanalysis region 126. The analysis region 126 limits the range of timingerrors that the receiver can measure, up to one-half of a symbol-time,but that should be more than sufficient range for most applications, asmentioned.

The receiver can determine both the sign and magnitude of thedisplacement 127 by calculating the difference between the signalsappearing in S1 and S3. Signal amplitudes depend on many factors such asunknown losses and gain settings. Therefore the A3−A1 difference may benormalized by calculating a signal ratio, such as dividing thedifference by A2, or even better by dividing the difference by the sumof the amplitudes received A1+A2+A3. The receiver can then determine thesign and magnitude of the timing error based on the normalized signalratio R=(A3−A1)/(A1+A2+A3), and can adjust its clock setting by thattiming error.

To consider a specific example, the difference in measured amplitude ofS1 and S3 is, say, 5% of the measured amplitude in S2. The magnitude ofthe adjustment time is then, approximately, 5% of the width of onesymbol-time. If the excess power appears in S1, the receiver's clock islate relative to the transmitter, and the receiver should reduce thereceiver's clock time by the indicated adjustment time, in this case 5%of one symbol-time. Hence the receiver can synchronize its clock withthe transmitter's clock according to the signal received in the threesymbol-times, without directly measuring a time displacement and withoutexchanging messages.

The time resolution achievable by this method depends on the backgroundnoise, the stability of the background noise across three symbol-times,and the amplitude resolution of the receiver, among other factors. Withgood SNR, the receiver is expected to resolve clock time errors of asmall fraction of the symbol-time, which should be sufficient for mostcases. Later examples show how to improve the time resolution further.

FIG. 1D is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a signal ratio, according tosome embodiments. As depicted in this non-limiting example, a functionalrelationship is graphed, relating the timing error ΔT (equal to adisplacement of the receiver's resource grid relative to the as-receivedtiming signal), versus a signal ratio R (which depends on the measuredamplitude received in each symbol-time A1, A2, and A3). The plot showsschematically a graph 199 of the signal ratio R=(A3−A1)/A2 versus thetime error ΔT. The letter “A” represents the example of FIG. 1A withzero timing error, “B” represents FIG. 1B with a small negative timingerror, and “C” represents FIG. 1C with a larger positive timing error.

The graph 199 is roughly linear, but with a small nonlinearity at largetime errors due to the division by A2. For large time errors, the amountof signal remaining in S2 decreases significantly due to the largedisplacement relative to the receiver's resource grid, and thisartificially increases R in the manner shown. Alternatively, thereceiver can divide by the sum of the magnitude signals in all threesymbol times, and thereby obtain a more linear relationship. In eithercase, the receiver can calculate an accurate correction from the graph199, and thereby correct the clock setting accordingly.

FIG. 1E is a flowchart showing an exemplary embodiment of a procedurefor performing synchronization, according to some embodiments. Asdepicted in this non-limiting example, at 161 a transmitter transmits atiming message spanning three symbol-times, at a pre-scheduled timeaccording to the transmitter's system clock. The first symbol-time isblank, with no transmission. The second symbol-time is transmitted as acontinuous uniform sine wave. The third symbol-time is again blank. Thetransmitter is powered so as to provide an abrupt turn-on at theboundary between the first and second symbol-times, and an abruptturn-off at the boundary between the second and third.

At 162, a receiver receives the timing signal. The receiver determinesthe amplitude or power received in each of the symbol-times. The symbolboundaries are determined by the receiver's clock. If the two clocksdisagree, the timing signal will be shifted from the central symbol-timeS2 into the first or last symbol-time S1 or S3. For example, thereceiver can determine the measured amplitude received in eachsymbol-time, termed A1, A2, and A3. If the receiver's clock issynchronized with the transmitter's clock, the A1 and A3 values shouldbe zero (or a low level due to background noise), and A2 should be ahigh level proportional to the transmitted signal amplitude. If thereceiver's clock is not synchronized with the base station's clock, thena part of the powered region will be shifted over to one of theinitially-blank symbol-times, which causes either A1 or A3 to haveadditional amplitude or power.

At 163, the receiver can calculate a ratio R equal to a differencebetween the measured amplitude in the first symbol-time minus the thirdsymbol-time, divided by the second symbol-time. (Alternatively, thedenominator could equal the sum of the three signals received in thethree symbol-times.) R is zero when the clocks are aligned. If theclocks are in disagreement, the timing signal is shifted into either S1or S3 depending on the sign of the clock disagreement.

At 164, based on the sign of R, the receiver can determine whether thereceiver's clock is ahead or behind the transmitter's clock. Thereceiver can also determine the magnitude of the clock error based onthe magnitude of R, for example using a predetermined relationship suchas that shown in FIG. 1D.

At 165, the receiver may arrange to avoid external signals encroachinginto S1 or S3, by discarding any signals received in the first half ofthe first symbol-time and the second half of the third symbol-time. Inother words, the receiver can choose to process only the signal in thesecond half of the first symbol-time, the entirety of the second symboltime, and the first half of the third symbol-time. The receiver maythereby avoid counting signals from extraneous message elements that mayencroach into the first and third symbol-times due to the timing error.If the timing signal is shifted into S1, for example, then an extraneousmessage element, from a symbol-time beyond S3, could partially spillover into S3, which would distort the R ratio. By ignoring any signalsin the first half of S1 and the last half of S3, the receiver can avoidsuch a problem.

At 166, the transmitter can transmit enhanced amplitude regions at thestart and end of the powered region, instead of a flat uniformamplitude. The enhanced amplitude regions may be configured and phasedto sharpen the turn-on and turn-off times. For example, the transmittercan transmit a brief period of enhanced amplitude at the beginning of S2to cause a rapid sharp turn-on, and a brief period of reversed amplitudeat the end of S2 to squelch the ringdown. The enhanced amplitude regionsat the start and end of the powered region may improve the timeresolution, especially for small time deviations, and may therebyprovide greater precision. The receiver may also, or alternatively,account for the edge transitions in analysis, by calibrating theremaining transition effect and adjusting the A1 and A3 measurementsaccordingly.

At 167, optionally, the receiver can correct its clock rate (orfrequency) to match that of the transmitter. The transmitter canbroadcast the timing signals periodically, or according to asynchronization schedule that the receiver knows. The receiver can thenmeasure the time interval between two timing signals (according to thereceiver's clock). If this value differs from the scheduled periodicity(according to the transmitter's clock), the receiver's clock rate hasdrifted. The frequency error is equal (to sufficient accuracy) to thecurrent clock frequency, times the measured interval minus the specifiedperiodicity, all divided by the specified periodicity.

Alternatively, the receiver can measure the timing error at each of thetwo successive timing signals, in which case the frequency error equalsthe difference between the two timing errors divided by the scheduledinterval between them, times the current frequency.

Importantly, the receiver has succeeded in aligning its clock with thetransmitter's clock, while avoiding unnecessary message exchangesbetween the transmitter and receiver, other than a single transmissionof the compact timing signal configured as shown in three symbol-times,two of which are unpowered. In addition, the base station of a networkcan arrange a synchronization schedule or periodicity, such as the firstthree symbol-times of the first subcarrier of each frame, therebyenabling all of the user devices in a network to synchronize their clocksettings every 10 milliseconds, without unnecessary messaging oroverhead. By comparing the amount of amplitude or power shifted into thenominally zero-power symbol-times S1 and S3, the receiver can determinethe timing error with higher precision than the legacy “first bit offirst octet” criterion, according to some embodiments.

FIG. 2A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times with “edge enhancements”, accordingto some embodiments. As depicted in this non-limiting example, a timingsignal 201 occupies three symbol-times S1, S2, S3, separated by symbolboundaries 205 of a resource grid 202. The timing signal 201 istransmitted with zero amplitude during the first symbol-time S1, apowered region 204 in S2, and another zero transmission in S3. Thepowered region 204 includes a brief amplitude enhancement 207 first,then a constant lower amplitude, followed by a second amplitudeenhancement 208 at the end of the second symbol-time. The amplitudeenvelope distribution 203 is also shown, without the oscillations. Theamplitude enhancements 207 208 provide finer time resolution at smallvalues of the timing error, since a small timing error causes arelatively large energy deposition into one of the adjacent symbol-timesS1 or S3.

If the receiver receives the timing signal 201 and finds that thepowered region 204 is centered between the S2 symbol boundaries 205,according to the receiver's resource grid structure, then the receivercan determine that the receiver's clock is synchronized with thetransmitter's clock. If the clocks are not synchronous, then the poweredregion 204 will be shifted left or right depending on whether thereceiver's clock is ahead or behind the transmitter's clock. Either theleading or trailing enhancement regions 207, 208 will be shifted intothe adjacent S1 or S3 symbol-time. Using the signal ratio calculated asR=(A3−A1)/A2, the edge enhancements 207, 208 at the start and end of thepowered region 204 cause R to increase rapidly for small time errors,and then slowly for larger time errors, as shown in the next figure.

FIG. 2B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with edgeenhancements, according to some embodiments. As depicted in thisnon-limiting example, the functional variation 299 of the signal ratio Rversus the time error ΔT, varies in a nonlinear fashion, with a rapidchange in R for small time errors, due to the amplitude enhancements,and a slower variation in R for larger time errors. Advantageously, withsuch a relationship between the time error and the ratio R, the receivermay detect time errors ranging from small to large, yet may retain highresolution for small time errors near zero due to the increased slope ofthe R distribution near zero.

FIG. 3A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times and “edge-pulses”, according to someembodiments. As depicted in this non-limiting example, a timing signal301, spans three symbol-times S1, S2, S3 of a resource grid 302 definedby symbol boundaries 305. The timing signal 301 has zero transmission inS1 and S3. In S2, the timing signal 301 includes two “edge pulses” whichare brief powered regions at the start and end of the S2 symbol-time,with zero transmission between. In other words, the central symbol-timeincludes three regions divided into the first edge-pulse 304 in thefirst region, zero transmission in the second region, and the lastedge-pulse in the third region. The amplitude envelope 303 is alsoshown.

A receiver can receive the timing signal 301, and measure theas-received signal A1, A2, A3 in each of the three symbol-times. Thereceiver can then determine a signal ratio R equal to the differencebetween A1 and A3, divided by A2. The receiver can thereby determine thetime error ΔT between the receiver's clock and the transmitter's clock.For example, if the receiver's clock is synchronized with thetransmitter, both S1 and S3 have zero signal, and hence R=0. If thereceiver's clock differs from the transmitter's clock, the position ofthe timing signal 301 will be shifted left or right, depending on whichclock is ahead, and is shifted by the amount of the timing error, andthis will cause some of the edge-pulse amplitude to be shifted into oneof the outer symbol-times S1 or S3. Because the edge-pulses 304 are muchshorter than the symbol-time, the signal ratio R rises rapidly with thetime error near zero. This rapid rise in R can thereby provide higherprecision for detecting small timing errors. For larger time errors, nofurther change is seen in R, after the edge-pulse 304 has passed by thesymbol boundary 305.

FIG. 3B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with edgepulses, according to some embodiments As depicted in this non-limitingexample, the distribution 399 of the signal ratio R versus the timingerror is shown for the previous example. For small timing errors, R hasa steep slope, whereas for larger timing errors, R remains constant. Dueto the rapid change in R versus timing error, the receiver can measuresmall timing errors, and can thereby adjust the receiver's clock to thetransmitter's clock more precisely.

FIG. 4A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times and a ramped amplitude, according tosome embodiments. As depicted in this non-limiting example, a timingsignal 401 spans three symbol-times of a resource grid 402, demarked insymbol boundaries 405. The timing signal 401 is zero amplitude in thefirst and third symbol-times S1 and S3, and has a “ramped” amplitude 404in the second symbol-time S2. The ramped amplitude 404 varies from ahigh value at the beginning of the second symbol-time, descending tozero at the center, and continuing in the opposite sense to a maximum atthe end of the second symbol-time. The envelope graph 403 shows theamplitude variation without the oscillations.

The receiver can measure the signal, such as the measured amplitude,received in each symbol-time, termed A1, A2, A3 and can calculate asignal ratio R equal to (A3+A1)/|A2|. The vertical bars representmagnitude, in this case the magnitude of the amplitude before averaging.The plus sign in the numerator is due to the phase reversal in theramped distribution. The receiver can then determine a direction andmagnitude of a clock error according to the ratio R.

FIG. 4B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a signal ratio with a rampedamplitude, according to some embodiments. As depicted in thisnon-limiting example, the signal ratio 499 is R=(A3+A1)/|A2| accordingto the example of FIG. 4A. Due to the ramped shape of the timing signal,the ratio R varies rapidly for small time deviations, and thereforeprovides high resolution near zero deviation, while also providingdetection of large deviations.

FIG. 5A is a schematic showing an exemplary embodiment of a timingsignal including two symbol-times and a uniform amplitude, according tosome embodiments. As depicted in this non-limiting example, a timingsignal 501 is shown as a uniform sine wave divided between twosymbol-times S1 and S2 of a resource grid 502 defined by symbolboundaries 505. Also shown is the envelope 503 of the timing signal 501.The timing signal 501 is initially at zero amplitude, but then about ⅔of the way through S1 it abruptly begins a powered region 504 at a highpower level, and continues about ⅓ of the way into S2, and then revertsto zero amplitude for the remainder of S2. Thus the powered portion 504of the timing signal 501 is about ⅔ of a symbol-time in duration and issymmetrically situated at a symbol boundary 505 between the twosymbol-times. The receiver is configured to discard energy received inthe first third of S1 and the last third of S2, and to analyze signalsin an analysis region 506 as indicated by dotted lines.

To detect a clock error, the receiver can determine the measuredamplitude of the timing signal 501 in each of the symbol-times S1 andS2. If the receiver's clock is synchronized with the base station'sclock, the powered region 504 of the timing signal 501 is equallydivided between S1 and S2. However, if there is a clock misalignment,the powered region 504 will be shifted to the left or right, causing oneof the two symbol-times to acquire more wave energy than the other. Thereceiver can calculate a signal ratio of the two symbol-times using aformula such as R=(A2−A1)/(A2+A1), that is, a difference between themeasured amplitude in the two symbol-times divided by the sum. Thisratio is sensitive to small shifts in timing between the transmitter andreceiver clocks. The receiver can normally measure the measuredamplitude in a symbol-time using the same signal processing as foramplitude demodulation, and may thereby obtain sufficient precision todetect small timing errors. Thus the receiver can detect small timingoffsets, and measure them quantitatively, by measuring amplitudes insymbol-times, and without performing unusual signal processing such asdetermining a time of an abrupt modulation change or other timestamppoint, and without exchanging synchronization messages (other than thebrief two-symbol timing signal 501). In effect, the timestamp point isthe center of the powered region 504. The position of the powered region504 is determined according to the distance of the timestamp point fromthe central symbol boundary 505.

An advantage of the depicted timing signal 501 may be that the timingsignal 501 is a uniform sine wave which is relatively easy for thetransmitter to transmit and for the receiver to receive. Anotheradvantage may be that the amplitude measurements in the two symbol-timesmay be relatively easy for the receiver to process and quantify, sincesuch signal processing is its normal function. Another advantage may bethat the timing signal 501 is compact, only two symbol-times long,further minimizing resource usage.

FIG. 5B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with a uniformamplitude, according to some embodiments. As depicted in thisnon-limiting example, a functional relationship 599 is shown relating atiming error to a signal ratio R=(A2−A1)/(A2+A1), according to thetiming signal 501 of the previous figure. Since the denominator includesthe entire powered section 504 of the timing signal 501, the functionalrelationship 599 is approximately linear until the timing error is solarge that the edge of the powered region 504 passes by the S1-S2 symbolboundary 505, after which R is constant. Hence the receiver candetermine the timing error by measuring the measured amplitudes receivedin the two symbol-times. No message exchanges or other legacy overheadare required.

FIG. 6A is a schematic showing an exemplary embodiment of a timingsignal including two symbol-times and a phase-flip amplitude, accordingto some embodiments. As depicted in this non-limiting example, a timingsignal 601 spans two symbol-times S1 and S2 of a resource grid 602 witha symbol boundary 605. The analysis region 606 is shown, and any signalsexterior to the dotted lines are discarded. The timing signal 601 isinitially at zero amplitude, then begins a powered region 604 of uniformamplitude, then has an abrupt phase reversal 607 centrally positioned inthe powered region 604, followed by another uniform amplitude region 608with reversed amplitude (or equivalently, reversed phase), followed byanother zero transmission region. The amplitude envelope 603 is alsoshown, indicating a positive amplitude region 604 abruptly changing to anegative amplitude region 608.

If the transmitter and receiver clocks are synchronized, the phasereversal 607 occurs at the boundary 605 between S1 and S2. If the clocksare not synchronized, a portion of the powered region 604 or 608 will beshifted out of S1 and into S2, or vice-versa, depending on the sign ofthe clock offset. Hence the receiver can determine the clock offset bymeasuring the measured amplitude A1 and A2 in the two symbol-times. Asmentioned, amplitude with reversed phase counts as negative amplitude.

FIG. 6B is a graph showing an exemplary embodiment of a functionalrelationship 699 between a timing error and a detection ratio with aphase-flip amplitude, according to some embodiments. As depicted in thisnon-limiting example, a clock time error ΔT is determined by the signalratio (A1+A2)/(|A1|+|A2|). The formula sign in the numerator reflectsthe opposite signs of the signal amplitudes in the first and secondregions 604, 608 of the previous example. In the denominator, themagnitude of the amplitude is determined and averaged in eachsymbol-time. By symmetry, the signal ratio is zero if the phase reversal607 is centered on the symbol boundary 605 between S1 and S2, and variesapproximately linearly for positive and negative timing errors.

FIG. 7A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times and a phase-flip amplitude,according to some embodiments. As depicted in this non-limiting example,a timing signal 701 spans three symbol-times S1, S2, S3 of a resourcegrid 702, with symbol boundaries 705 between symbol-times. The timingsignal 701 is initially at zero amplitude in S1, then in S2 is a uniformamplitude 704 for one-half of a symbol-time, and abruptly changes at 707to the opposite phase (or amplitude) in the middle of S2, followed byanother uniform amplitude region 708 at negative amplitude, and thenzero amplitude in S3. The amplitude envelope 703 is also shown. Theanalysis region 706 extends from the middle of S1 to the middle of S3 asindicated by dotted lines. The exterior regions are discarded by thereceiver.

If the receiver clock is synchronized with the transmitter, the phasereversal 707 will be centered in S2 and the measured amplitude will bezero in all three symbol-times. If the receiver's clock is misalignedwith the transmitter, then the timing signal 701 will be shifted left orright, thereby causing a portion of the powered portion 704 or 708 toappear in either S1 or S3. The receiver can determine the measuredamplitude in all three symbol-times A1, A2, A3 and thereby measure thetiming error. For example, the receiver can calculate a signal ratio Requal to (A3+A1)/(|A1|+|A2|+|A3|) where the numerator sign reflects theamplitude signs, and vertical bars represent magnitude. Using thatsignal ratio, or another equivalent formula, the receiver can measurethe sign and magnitude of the timing error according to the measuredamplitude in the three symbol times.

FIG. 7B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio with aphase-flip amplitude, according to some embodiments. As depicted in thisnon-limiting example, a functional relationship 799 between a timingerror ΔT and a signal ratio R, as described in the previous example,produces a linear relationship as shown. When the timing error becomeslarge enough for the phase reversal 707 to finally pass by one of thesymbol boundaries 705 of S2, the signal ratio R begins to decrease dueto the accumulation of opposite-sign amplitude in either S1 or S3.Throughout the linear region, the receiver can determine the timingerror by measuring the measured amplitudes in the three symbol-times.

FIG. 8A is a schematic showing an exemplary embodiment of a timingsignal including three symbol-times, end-pulses, and a phase-flipamplitude, according to some embodiments. As depicted in thisnon-limiting example, a timing signal 801 spans three symbol-times S1,S2, S3 separated by symbol boundaries 805 in a resource grid 802. Thetiming signal 801 includes two separate amplitude regions 804, 808. Eachof the amplitude regions includes a central phase inversion 807 so thatthe amplitude before the phase inversion is opposite to the amplitudeafter the phase inversion. Also shown is an amplitude envelope 803. Thephase-reversed signal is shown as a negative amplitude. Dotted linesshow the limits of the analysis region 806.

When the receiver clock is synchronized with the transmitter clock, thetwo phase inversions 807 are coincident with the two symbol boundaries805 of S2. If the receiver clock disagrees with the transmitter clock,the timing signal 805 is shifted relative to the receiver's symbolboundaries, which alters the amplitudes measured by the receiver in thethree symbol times. For example, if the receiver clock is behind thetransmitter clock, the timing signal 801 will arrive too soon, causingthe first amplitude region 804 to shift from S1 partially towards S2,and the amplitude region 808 to shift from S2 partially into S3. Thereceiver would then measure a lower positive measured amplitude in S1,an increasingly negative measured amplitude in S2, and an increasinglypositive amplitude in S2. If the timing error is reversed, the amplitudechanges are also reversed. The receiver can measure the amplitude A1,A2, A3 in the three symbol-times, and can then accumulate the timingchanges in a signal ratio R equal to (A3+A1)/(|A1|+|A2|+|A3|) which iszero when the two clocks are synchronized.

FIG. 8B is a graph showing an exemplary embodiment of a functionalrelationship between a timing error and a detection ratio withend-pulses and a phase-flip amplitude, according to some embodiments. Asdepicted in this non-limiting example, a the functional relationship 899between the timing error and the signal ratio of the previous exampleincludes a linear central region corresponding to portions of theamplitude regions 804, 808 shifting across the S2 symbol boundaries 805.For larger displacements, R becomes a flat response after the amplituderegion has completely passed the symbol boundary. By measuring just thethree average amplitudes A1, A2, A3 in the three symbol-times, thereceiver can determine the timing error. In addition, since in this casethere are two timestamp points at the two S2 boundaries, noiseconditions that change in time may be averaged in the signal ratio,thereby providing a more accurate measure of the timing error.

Due to the many options and variations disclosed herein, and otherversions derived therefrom by artisans after reading this disclosure, itwould be helpful for a wireless standards committee to establishconventions governing formats and implementation options for providingcompact timing signals and ultra-lean procedures for precisionsynchronization, as disclosed. Such beneficial timing and frequencyalignment procedures may enable users to communicate in 5G and 6Gmulti-GHz bands with increased reliability, while avoiding unnecessarymessaging and delays.

The wireless embodiments of this disclosure may be aptly suited forcloud backup protection, according to some embodiments. Furthermore, thecloud backup can be provided cyber-security, such as blockchain, to lockor protect data, thereby preventing malevolent actors from makingchanges. The cyber-security may thereby avoid changes that, in someapplications, could result in hazards including lethal hazards, such asin applications related to traffic safety, electric grid management, lawenforcement, or national security.

In some embodiments, non-transitory computer-readable media may includeinstructions that, when executed by a computing environment, cause amethod to be performed, the method according to the principles disclosedherein. In some embodiments, the instructions (such as software orfirmware) may be upgradable or updatable, to provide additionalcapabilities and/or to fix errors and/or to remove securityvulnerabilities, among many other reasons for updating software. In someembodiments, the updates may be provided monthly, quarterly, annually,every 2 or 3 or 4 years, or upon other interval, or at the convenienceof the owner, for example. In some embodiments, the updates (especiallyupdates providing added capabilities) may be provided on a fee basis.The intent of the updates may be to cause the updated software toperform better than previously, and to thereby provide additional usersatisfaction.

The systems and methods may be fully implemented in any number ofcomputing devices. Typically, instructions are laid out on computerreadable media, generally non-transitory, and these instructions aresufficient to allow a processor in the computing device to implement themethod of the invention. The computer readable medium may be a harddrive or solid state storage having instructions that, when run, orsooner, are loaded into random access memory. Inputs to the application,e.g., from the plurality of users or from any one user, may be by anynumber of appropriate computer input devices. For example, users mayemploy vehicular controls, as well as a keyboard, mouse, touchscreen,joystick, trackpad, other pointing device, or any other such computerinput device to input data relevant to the calculations. Data may alsobe input by way of one or more sensors on the robot, an inserted memorychip, hard drive, flash drives, flash memory, optical media, magneticmedia, or any other type of file-storing medium. The outputs may bedelivered to a user by way of signals transmitted to robot steering andthrottle controls, a video graphics card or integrated graphics chipsetcoupled to a display that maybe seen by a user. Given this teaching, anynumber of other tangible outputs will also be understood to becontemplated by the invention. For example, outputs may be stored on amemory chip, hard drive, flash drives, flash memory, optical media,magnetic media, or any other type of output. It should also be notedthat the invention may be implemented on any number of different typesof computing devices, e.g., embedded systems and processors, personalcomputers, laptop computers, notebook computers, net book computers,handheld computers, personal digital assistants, mobile phones, smartphones, tablet computers, and also on devices specifically designed forthese purpose. In one implementation, a user of a smart phone orWi-Fi-connected device downloads a copy of the application to theirdevice from a server using a wireless Internet connection. Anappropriate authentication procedure and secure transaction process mayprovide for payment to be made to the seller. The application maydownload over the mobile connection, or over the Wi-Fi or other wirelessnetwork connection. The application may then be run by the user. Such anetworked system may provide a suitable computing environment for animplementation in which a plurality of users provide separate inputs tothe system and method.

It is to be understood that the foregoing description is not adefinition of the invention but is a description of one or morepreferred exemplary embodiments of the invention. The invention is notlimited to the particular embodiments(s) disclosed herein, but rather isdefined solely by the claims below. Furthermore, the statementscontained in the foregoing description relate to particular embodimentsand are not to be construed as limitations on the scope of the inventionor on the definition of terms used in the claims, except where a term orphrase is expressly defined above. Various other embodiments and variouschanges and modifications to the disclosed embodiment(s) will becomeapparent to those skilled in the art. For example, the specificcombination and order of steps is just one possibility, as the presentmethod may include a combination of steps that has fewer, greater, ordifferent steps than that shown here. All such other embodiments,changes, and modifications are intended to come within the scope of theappended claims.

As used in this specification and claims, the terms “for example”,“e.g.”, “for instance”, “such as”, and “like” and the terms“comprising”, “having”, “including”, and their other verb forms, whenused in conjunction with a listing of one or more components or otheritems, are each to be construed as open-ended, meaning that the listingis not to be considered as excluding other additional components oritems. Other terms are to be construed using their broadest reasonablemeaning unless they are used in a context that requires a differentinterpretation.

1. A method for a user device of a wireless network to synchronize aclock of the user device with a clock of a base station of the wirelessnetwork, the method comprising: a) receiving, from the base station,three temporally successive resource elements comprising a firstresource element, a second resource element, and a third resourceelement, of a resource grid comprising subcarriers in frequency andsymbol-times in time; b) wherein the first resource element comprises afirst signal, the second resource element comprises a second signal, andthe third resource element comprises a third signal; c) measuring afirst energy of the first signal, a second energy of the second signal,and a third energy of the third signal; d) determining a signaldifference comprising the first energy minus the third energy; e)determining a ratio comprising the signal difference divided by thesecond energy; f) determining, according to the ratio, a timing offset;and g) causing the clock of the user device to be synchronized with theclock of the base station by subtracting the timing offset from theclock of the user device.
 2. The method of claim 1, wherein the threetemporally successive resource elements are received according to 5G or6G technology.
 3. The method of claim 1, further comprising: a)determining the first energy by averaging a received amplitude or poweracross the first resource element; b) determining the second energy byaveraging a received amplitude or power across the second resourceelement; c) determining the third energy by averaging a receivedamplitude or power across the third resource element.
 4. The method ofclaim 1, wherein the first and third resource elements are transmitted,by the base station, with no transmission therein.
 5. The method ofclaim 1, wherein the second resource element is transmitted, by the basestation, with a transmitted signal comprising a uniform amplitude. 6.The method of claim 1, wherein the second resource element istransmitted, by the base station, with a transmitted signal comprising anon-uniform amplitude, wherein the non-uniform amplitude has a highertransmitted amplitude at a beginning and an ending of the secondresource element, and a lower transmitted amplitude, lower than thehigher transmitted amplitude, in a middle of the second resourceelement.
 7. The method of claim 1, wherein the second resource elementis transmitted, by the base station, with a transmitted signalcomprising two spaced-apart pulses of transmission, wherein a firstpulse of the two spaced-apart pulses is transmitted at a beginning ofthe second resource element, and a second pulse of the two spaced-apartpulses is transmitted at an ending of the second resource element. 8.The method of claim 1, wherein the second resource element istransmitted, by the base station, with a transmitted signal comprising anon-uniform amplitude, wherein the non-uniform amplitude is rampedlinearly from a high value at a beginning of the second resourceelement, through zero amplitude at a middle of the second resourceelement, to the high value at an ending of the second resource element.9. A method for a user device of a wireless network to synchronize aclock of the user device with a clock of a base station of the wirelessnetwork, the method comprising: a) receiving, from the base station, twotemporally successive resource elements comprising a first resourceelement and a second resource element, of a resource grid comprisingsubcarriers in frequency and symbol-times in time; b) wherein the firstresource element comprises a first signal and the second resourceelement comprises a second signal; c) measuring a first signed amplitudeof the first signal and a second signed amplitude of the second signal;d) determining a signal difference comprising the first signed amplitudeminus the second signed amplitude, and a signal sum comprising the firstsigned amplitude plus the second signed amplitude, wherein a signedamplitude is an average amplitude at a particular phase, averaged acrossa symbol-time; e) determining a ratio according to the signal differenceand the signal sum; f) determining, according to the ratio, a timingoffset; and g) causing the clock of the user device to be synchronizedwith the clock of the base station by subtracting the timing offset fromthe clock of the user device.
 10. The method of claim 9, wherein: a) thefirst signal is transmitted, by the base station, with zero amplitude ina first half of the first resource element, followed by a non-zeroamplitude in a second half of the first resource element; and b) thesecond signal is transmitted, by the base station, with the non-zeroamplitude in a first half of the second resource element, followed byzero amplitude in a second half of the second resource element.
 11. Themethod of claim 10, wherein the ratio comprises the signal differencedivided by the signal sum.
 12. The method of claim 9, wherein: a) thefirst signal is transmitted, by the base station, with zero amplitude ina major fraction of the first resource element, followed by a non-zeroamplitude in a minor fraction of the first resource element; and b) thesecond signal is transmitted, by the base station, with the non-zeroamplitude in the minor fraction of the second resource element, followedby zero amplitude in the major fraction of the second resource element;c) wherein the major fraction is larger than the minor fraction.
 13. Themethod of claim 12, wherein the ratio comprises the signal differencedivided by the signal sum.
 14. The method of claim 9, wherein: a) thefirst signal is transmitted, by the base station, with zero amplitude ina first half of the first resource element, followed by a non-zeroamplitude in a second half of the first resource element; and b) thesecond signal is transmitted, by the base station, with the non-zeroamplitude in a first half of the second resource element followed byzero amplitude in a second half of the second resource element; c)wherein the first signal is transmitted with the particular phase, andthe second signal is transmitted with an inverted phase comprising theparticular phase plus 180 degrees.
 15. The method of claim 14, whereinthe ratio comprises the signal sum divided by the signal difference. 16.A method for a receiver of a wireless network to synchronize with a basestation of the wireless network, the method comprising: a) receiving,from the base station, four temporally successive resource elementscomprising a first resource element, a second resource element, a thirdresource element, and a fourth resource element of a resource gridcomprising subcarriers in frequency and symbol-times in time; b) whereinthe first resource element comprises a first signal, the second resourceelement comprises a second signal, the third resource element comprisesa third signal, and the fourth resource element comprises a fourthsignal; c) measuring a first signed amplitude of the first signal, asecond signed amplitude of the second signal, a third signed amplitudeof the third signal, and a fourth signed amplitude of the fourth signal;d) determining a signal difference comprising the second signedamplitude minus the third signed amplitude, and a signal sum comprisingthe second signed amplitude plus the third signed amplitude; e)determining a ratio according to the signal difference and the signalsum; f) determining, according to the ratio, a timing offset; and g)causing the clock of the user device to be synchronized with the clockof the base station by subtracting the timing offset from the clock ofthe user device.
 17. The method of claim 16, wherein: a) the firstsignal is transmitted, by the base station, with zero amplitude therein;b) the second signal is transmitted, by the base station, with zeroamplitude in a particular fraction of the second resource element,followed by a non-zero amplitude in a specific fraction of the secondresource element, wherein the specific fraction equals 1 minus theparticular fraction; c) the third signal is transmitted, by the basestation, with the non-zero amplitude in the specific fraction of thethird resource element, followed by zero amplitude in the particularfraction of the third resource element; and d) the fourth signal istransmitted, by the base station, with zero amplitude in the fourthresource element.
 18. The method of claim 17, wherein the ratiocomprises the signal difference divided by the signal sum.
 19. Themethod of claim 16, wherein: a) the first signal is transmitted, by thebase station, with zero amplitude therein; b) the second signal istransmitted, by the base station, with zero amplitude in a particularfraction of the second resource element, followed by a non-zeroamplitude in a specific fraction of the second resource element, whereinthe specific fraction equals 1 minus the particular fraction; c) thethird signal is transmitted, by the base station, with the non-zeroamplitude in the specific fraction of the third resource element,followed by zero amplitude in the particular fraction of the thirdresource element; and d) the fourth signal is transmitted, by the basestation, with zero amplitude therein; e) wherein the second signal istransmitted with a particular phase, and the third signal is transmittedwith the particular phase plus 180 degrees.
 20. The method of claim 19,wherein the ratio comprises the signal sum divided by the signaldifference.